diketahui f(x)=1/x-1, x≠1 dan g^-1(x)=1-x/x, x≠0 jika h(x)=(gof)(x) fungsi h^-1(2x+1)=

Mapel : Matematika
Kelas : X SMA
Bab : Fungsi Komposisi dan Fungsi Invers

Pembahasan :
f(x) = 1/(x - 1)

G^-1(x) = (1 - x)/x
x = (1 - y)/y
xy = 1 - y
xy + y = 1
y(x + 1) = 1
y = 1/(x + 1)
g(x) = 1/(x + 1)

h(x) = Gof(x)
h(x) = g(f(x))
h(x) = 1/[1/(x - 1) + 1]
h(x) = (x - 1)/x
h(2x + 1) = (3x)/(2x + 1)

h(2x + 1) = y
3x/(2x + 1) = y
3x = 2xy + y
3x - 2xy = y
x(3 - 2y) = y
x = y/(3 - 2y)
h^-1(2x + 1) = x/(3 - 2x)